1. Place apples in a large stockpot and add enough water cover by at least 2 inches.
2. Stir in sugar, cinnamon, and allspice. Bring to a boil.
3. Boil, uncovered, for 1 hour.
4. Cover pot, reduce heat and simmer for 2 hours.
5. Strain apple mixture through a fine-mesh sieve. Discard solids.